Apparatus for titration flow injection analysis

ABSTRACT

A method for titration flow injection analysis by introducing a multicomponent sample into a carrier stream which flows into a mixing/sensing cell and titrating with a reactant more than one component of the sample by sensing a plurality of endpoints. The apparatus of the invention includes a stirring means within the mixing/sensing cell which generates helical flow within the cell so that bubbles are not retained in the cell.

This is a continuation of application Ser. No. 254,502, filed Oct. 6,1988, now abandoned, which is a continuation of application Ser. No.932,811, filed Nov. 19, 1986, now U.S. Pat. No. 4,798,803, which is acontinuation-in-part of application Ser. No. 512,797, filed July 11,1983, now abandoned which is a continuation-in-part of Ser. No. 753,750filed 7/10/85, abandoned.

FIELD OF THE INVENTION

This invention relates to a new apparatus and method for improved flowinjection titrimetry analysis.

BACKGROUND OF THE INVENTION

The need for repeatable accurate chemical analysis methods and apparatusis ever increasing. In response to this need, a variety of analyzershave been built. With each new analyzer, the focus has consistently beenon the construction of analysis apparatus which increases analysisapparatus capacity and reduces the number of required steps in theanalysis process. Flow injection analyzers have been built to meet theseneeds.

Flow injection analyzers are instruments capable of detecting featuresof a sample injected into a continuously flowing solution. Flowinjection analysis is based on an analysis system capable of forming areproducible gradient of sample in a reagent flow, detectable as agradient curve. Measurements carried out on the resultant gradient curveare used to determine the characteristics and components of the sample.

A new area in the field of flow injection analysis is flow injectiontitrimetry (F.I.T.) which combines the best features of flow injectionanalysis with titrimetry techniques.

Flow injection titrimetry is derived from titration which is thevolumetric determination of a constituent in a known volume of asolution by the slow addition of a standard reacting solution of a knownstrength until the reaction is completed. Completion of the reaction isfrequently indicated by a color change (indicator) or electrochemicalchange in the solution.

Flow injection titrimetry (F.I.T.) has been developed to produce rapid,simple, reliable, versatile and accurate analysis systems for processcontrol applications. Different from other flow injection analysistechniques, flow injection titrimetry is based on the measurements ofpeak width rather than peak height. The width of this peak isproportional to the log of the sample concentration. Contrary to otherflow injection analysis techniques, flow injection titrimetry makes useof a large sample dispersion to create a concentration gradient overtime. This concentration gradient is known as the "exponentialconcentration gradient". The exponential concentration gradient is theconcentration gradient within the mixing cell during flow injectionanalysis.

The concept of single point titration using flow injection analysistechniques has been described for acid/base systems by Ove Åstrm'sarticle, "Single-Point Titrations" found in Analytica Chimica Acta, 105(1979) 67-75. The Åstrom method for a single-point titrimetric systemfor acids and bases utilizes a reaction cell consisting of a referenceelectrode, a glass electrode, a mixing coil 300 cm long, and tefloninjection tubing. Only one analysis can be performed using the reactioncell with detection electrodes. A need has long been felt for a dualanalysis system.

Multielement trace analyzers using nonsegmented continuous flow analysishave been described in "Correspondence", Analytical Chemistry, Vol. 50,No. 4. (1978) 654-656. However, this analysis technique is taught inonly a very general way. The multielement trace analysis usingnonsegmented continuous flow for the compounds 4-(2-pyridylazo)resorcinol (PAR), lead (II) and vanadium (V) is colorimetric rather thantitrimetric. No specific teaching of multielement trace analysis usingflow injection titrimetry has been found, particularly forcaustic/carbonate systems.

The apparatus used in multielement trace analysis, generally hasincluded a reaction cell, a measuring instrument, and a recorder or dataprocessing unit, see, "Injection Technique In Dynamic Flow-ThroughAnaylsis With Electroanalytical Sensors" by Pungor, Feher, Nagy, Toth,Horvai and Gratzl, appearing in Analytica Chemica Acta, 109 (1979),1-24. This apparatus has not been capable of both acting as a reactioncell and a detection cell for multiple endpoint flow injectiontitrimetry. The present invention seeks to provide such an instrumentand an accompanying flow injection titrimetry technique.

Known analysis methods have utilized batch analysis methods fordetecting endpoints of independently titratable species incaustic/carbonate reactions. One batch technique, as described inScotts', Standard Methods of Chemical Analysis (5th Ed., p. 2256)describes a double-endpoint determination of sodium hydroxide and sodiumcarbonate in a mixture thereof by (a) titrating with sulfuric acid tothe phenolphthalein endpoint (NaOH converted to NaHSO₄ and H₂ O; Na₂ CO₃converted to NaHCO₃) and (b) titrating further with sulfuric acid to themethyl-orange endpoint (NaHCO₃ converted to NaHSO₄, CO₂ and H₂ O).However, batch techniques have numerous drawbacks since they are notcapable of continuous quantitative measurements nor continuous titrationanalysis. The batch titrations must be periodically stopped and thereactors must be cleaned after each reaction is completed. This knowntechnique has required abundant analysis time to obtain the necessaryresults. A need has existed for determining multiple end points ofindependently titratable species in a continuous flow, nonbatch type oftitration system.

Known continuous flow injection analysis techniques have been developedfor continuous flow acid-base titration as described in J. Ruzicka, andE. H. Hansen, Flow Injection Analysis, Wiley-Interscience Publication,(Chemical Analysis, Vol. 62), 1981. With the batch tank model developedby Ruzicka et al., the time span between these two observed equivalencepoints, t_(eq), may be expressed by the following equation: ##EQU1##where V_(m) is the mixing cell volume which is much larger than thesample volume, V_(s), C_(so) is the concentration of S in the mixingcell at t=0, Q_(s) is the sample flow rate, and Q_(t) is the titrantflow rate and thus ##EQU2## where C_(s) ^(@) is the initialconcentration of S. With a single channel manifold as used in this work,

    Q.sub.s =Q.sub.t =Q                                        (3)

and the above equation reduces to ##EQU3## where C_(t) is theconcentration of the titrant. Therefore, for the titration of base withan acid ##EQU4## where n is the number of equivalents weight of theacid. Rearranging this equation and substituting the equation forC_(so), a linear equation is obtained with the form of

    ln.sub.e C.sub.base =K.sub.1 t.sub.eq +k.sub.2.            (6)

The slope of the response curve is affected by V_(m) and Q. Theintercept, and thus the lower limit of detection, is affected by V_(s),V_(m), and C_(acid). Thus if V_(s) and V_(m) are kept constant, thesensitivity of the method can be changed by varying Q; and the lowerlimit of detection can be changed by varying C_(acid). Flow injectiontitrimetry methods are capable of providing detection limitsensitivities which can be chosen to fit the needs of the analyst.

A problem with the above described single channel system is that theresults were limited to the analysis of one component, that is, whereC_(s) is the molar concentration of species to be titrated; K is theconstant related to the apparatus including cell volume and flow rate;t_(eq) is the time to an equivalence point, i.e., t_(i) ; C is theconstant relating concentration of the titrant; V_(m) is the volume inthe mixing cell; and Q is the flow rate then:

    ln.sub.e C.sub.s =Kt.sub.eq +C                             (7)

    C.sub.s =ln.sub.e.sup.-1 (Kt.sub.eq +C)                    (8)

    ln.sub.e C.sub.s =Q/V.sub.m t.sub.eq +ln.sub.e C           (9)

Ruzicka and Hansen also developed another titration system, described in"Recent Developments in Flow Injection Analysis: Gradient Techniques andHydrodynamic Injection", Analytica Chimica Acta, 145 (1983), 1-15.However, this continuous flow multiple endpoint titration system islimited to a teaching for a single component acid-base titration. Inparticular, the authors focus on the titration of phosphoric acid by1×10⁻³ M sodium hydroxide, and do not address a multiple component flowinjection analysis multiple endpoint system.

Yet another flow injection titrimetry technique was taught in U.S. Pat.No. 4,283,201 to DeFord et al. In that reference, a titrant is suppliedto two parallel fluidly communicating circuits. The first circuitinvolved a pressure regulator means and a flow restricting meansterminating in a first electrical conductivity detection cell meanshaving a vent means. The second circuit involved a flow rate controllermeans, a sample valve means and a chromatograph column or equivalentmeans terminating in a second electrical conductivity detection cellmeans also having a vent means. The electrical output signalsrepresenting the electrical conductivity of the fluid conducted throughthe first cell means and the second cell means were combined in anelectrical difference detection means. The electrical output signalgenerated within the detection means and representative of thedifference in the two fluid conductivities was passed to one channel ofa dual channel strip chart recording means and additionally passed to anelectrical signal derivative detection means. The electrical outputsignal, representative of the derivative of said difference signal, wasthen passed to a digital clock and counter means and then to a recordingmeans. The material or sample to be reacted or titrated was supplied tothe two parallel fluidly communicating circuits from a third conduit.

The DeFord teaching provided a method and apparatus for flow injectiontitrimetry which used a plurality of reactant streams, analyzers, anddetection apparatus to detect a plurality of end points of a complexsample. This teaching has not satisfied all the needs of the medical,pharmaceutical and argicultural fields in regard to analysis apparatus.A need exists for a flow injection method of analysis which providesdata regarding a plurality of end points requiring less equipment andless time than the DeFord teaching. A method and device have long beenneeded for performing multiple endpoint titrations in a single analysis.The present invention seeks to go beyond these teachings and present amethod of nonlinear multiple endpoint flow injection titrimetry forseveral species of sample.

One problem with prior mixing cells for titration flow injectionanalysis is entrapment of bubbles in the mixing cell. This problem isrelated to the mixing action of the stirrer in the mixing cell. Bubblestend to collect on cell walls and to remain in the vortex of the stirredcontents of the cell and interfere with analytical accuracy. Specialstirrers such as the Fisher Scientific stir bar for spectrophotometercells, Catalog No. 14-511-72, are designed to minimize aeration and areeffective in spectrophotometric cuvettes. They are, however, inadequatein Flow Injection titration analysis because of a demonstrated tendencyto form and trap bubbles on the stirrer itself and on the tip of thedetector probe. The trapped bubbles interfere with the analyticalaccuracy. The stirrer of the present invention results in helical flowof the carrier from the inlet to the outlet of the mixing cell with aminimum of vertical mixing (assuming vertical progression of helicalflow in the mixing cell). This helical flow, preferably in combinationwith a chamber which is narrowed near the outlet of the chamber to allowbubble coalescing which facilitates bubble removal from the cell andeffectively solves the above mentioned bubble problem.

SUMMARY OF THE INVENTION

The present invention provides a method for determining the titrationendpoints of at least two independent titratable species by flowinjection analysis of a single sample, comprising the steps of:providing a stream of carrier; introducing a multicomponent sample intothe carrier stream; flowing the sample into a mixing and detection cellat a defined carrier flow rate; forming an exponential dilution gradientwithin the mixing and detection cell; titrating with a reactant, eachspecies of the sample mixture, in the mixing cell, to a plurality of endpoints; determining the concentration of each species of the sample inthe mixing cell by forming a relationship between the time of titratingeach species to an equivalence point using the multicomponent systemrelationship expressed as:

    Tln(RF.sub.i)=t.sub.i +TlnC.sub.t,                         (10)

developed from the equations:

    t.sub.i =Vm/Qln(Vs/Vm)-ln C.sub.t ]+Vm/Qln(Sn.sub.i C.sub.i)(11)

wherein:

t_(i) are the times to titration endpoints;

V_(s) is the volume of the sample;

V_(m) is the mixed cell volume;

Q is the flow rate;

C_(i) are the molar concentrations of each titratable species in thesample;

n_(i) are the number of equivalents of each titratable species in thesample;

R is the ratio of sample volume to cell volume;

T is the average cell residence time of titrant;

F_(i) are the sample concentration functions corresponding to therelationships between the concentrations of C_(i), as controlled by thestoichiometry of the species/titrant reactions; and

C_(t) is the molar concentration of titrant.

The invention method further comprises the step of using at least twoacid base neutralization reactions which occur during the same timeinterval, during titration of each species of the sample mixture toobtain a plurality of endpoints.

The method invention can be used for the multiple-endpoint titration ofthe following caustic/carbonate system:

    n.sub.1 NaOH+n.sub.1 HCL→n.sub.1 NaCl+n.sub.1 H.sub.2 O(12)

    n.sub.2 Na.sub.2 CO.sub.3 +n.sub.2 HCl→n.sub.2 NaHCO.sub.3 +n.sub.2 NaCl                                                      (13)

wherein at t₁ :

n₁ moles of NaOH=C₁, and

n₂ moles of Na₂ CO₃ =C₂

such that:

F₁ =C₁ +C₂.

    n.sub.2 NaHCO.sub.3 +n.sub.2 HCl→n.sub.2 NaCl+n.sub.2 CO.sub.2 +n.sub.2 H.sub.2 O                                        (14)

wherein at t₂ :

n₁ moles of NaOH=C₁

n₂ moles of Na₂ CO₃ =C₂, and

n₂ moles of NaHCO₃ is equivalent to the concentration of C₂ such that:

F₂ =C₁ +2C₂

to simultaneously determine a plurality of end points.

Alternatively, the method of the invention may further comprise the stepof using at least two reduction or oxidation reactions which occurduring the same time interval, during titration of each species of thesample mixture to obtain a plurality of endpoints.

The invention yet further involves a mixing cell for titration flowinjection analysis, comprising:

a body defining a chamber having a lower inlet port to said chamber andan upper outlet port from said chamber; a sensing means within saidchamber placed between said inlet and outlet ports; a stirring meanseffective to generate helical flow of a liquid flowing into said inletport to said outlet port in said chamber so that bubbles in said liquidare not retained in said chamber at said detection means.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic of the preferred embodiment of the apparatusinvention.

FIG. 2 is a cross section of the embodiment shown in FIG. 1, taken alongthe cutting line 2--2.

FIG. 3 is a graphic representation of data obtained by the method of thepresent invention.

DETAILED DESCRIPTION OF THE INVENTION

More particularly, the invention achieves a reaction between a sampleand a titrant wherein equivalence points are reached such that

    t.sub.1 =Vm/Q[ln(Vs/Vm)-ln C.sub.t ]+Vm/Q ln (C.sub.1 +C.sub.2)(15)

    and

    t.sub.2 =Vm/Q[ln(Vs/Vm)-ln C.sub.t ]+Vm/Q ln (C.sub.1 +2C.sub.2)(16)

wherein:

t₁ is the time to the equivalence point of the first species;

t₂ is the time to the equivalence point of the second species;

V_(s) is the volume of the sample;

V_(m) is the mixed cell volume;

Q is the flow rate;

C₁ is the molar concentration of the first species; and

C₂ is the molar concentration of the second species.

If a sample plug with concentration C_(s) is injected into a flowingstream of titrant with concentration C_(t) and then passed into a mixingcell, and if the mixing and chemical reactions are instantaneous, anexponential concentration gradient is formed. The exponentialconcentration gradient of the sample and titrant mixture is then passedin the cell to a detector where two or more signal transitions areobtained. These signal transitions are the points at which there is asignificant change in the concentration of a monitored species such aspH. The first signal change marks the effective start of the titration.Other signal changes mark the passage of titration equivalent pointsdescribed by a sudden change in, for example, the carrier pH; and in thecase of a single titration species, the end of the titration. Changes inpH may be easily detected with a pH electrode. Other titratable speciesmay be detected using similar sensors (e.g. ion-selective electrodes oramperometric means).

One embodiment of the apparatus invention is shown in FIGS. 1 and 2. Theapparatus includes a mixing cell having a body 12 defining a chamber 14.Disposed within the chamber 14 is a stirrer 16. The stirrer 16 serves adual function within the chamber 14; (1) by mixing the reagent fluidwith the sample to promote a reaction and (2) by forcing the fluid toflow in a helical manner upwards through the chamber with a maximum ofrotational mixing but with a minimum of up and down mixing so thatbubbles do not remain in the chamber 14. A preferred stirrer 16 is aSpinfin type, sold by Ace Scientific, of East Brunswick, N.J., which hasbeen modified by removal of the top fins and addition of side slots 17(one of which is shown in FIG. 1). Other stirring means, such as devicesincluding stirrers mounted on rotating shafts, may be used as long asthey provide for helical flow, and do not trap bubbles.

The body 12 has a lower inlet port 18 and an upper outlet port 20. Asensing means 22 is disposed within the chamber 14. The sensing meanscan be a pH electrode, an ion specific electrode, or generally anyamperometric or potentiometric sensing electrode. A narrowing of thechamber 14 near the outlet port 20 results in a gas trap 24 for trappingbubbles formed during the multiple endpoint titration in the chamber 14.The chamber 14 is designed to provide helical flow between the inletport 18 and the sensing means 22 whereas the gas trap 24 is designed toprovide laminar flow, and collect and dispose of any gas bubbles formedduring the reaction. The trap 24 is positioned at the top of chamber 14near the outlet port 20 to prevent gas bubbles disrupting thetitrametric measurements being taken. The outlet port 20 may bepositioned from the bottom to the top of the gas trap 24, but ispreferably positioned at the top as shown in FIG. 1.

Typical results for caustic/carbonate systems using the inventive methodand apparatus are depicted in the Table I and in FIG. 3 for thefollowing multicomponent system wherein:

C_(s) =Sample Concentration

C_(t) =Titrant Concentration

R=Sample Volume/Cell Volume Ratio

T=Average Cell Residence Time of Titrant

and

    Tln(RF.sub.i)=t.sub.i +Tln C.sub.t                         (17)

where:

t_(i) =Time to equivalence Point i

F_(i) =Sample Concentration Function

Corresponding to Point i then, for the caustic/carbonate system:##STR1##

    n.sub.2 NaHCO.sub.3 +n.sub.2 HCl→n.sub.2 NaCl+n.sub.2 CO.sub.2 +n.sub.2 H.sub.2 O}t.sub.2                                (20)

and for:

Titrated species at time t₁ :

n₁ moles of NaOH (Concentration=C₁) and

n₂ moles of Na₂ CO₃ (Concentration=C₂)

for a concentration function at t₁ of F₁ =C₁ +C₂ ;

and for:

Titrated species at time t₂ :

n₁ moles of NaOH (Concentration=C₁) and

n₂ moles of Na₂ CO₃ (Concentration=C₂)

for a concentration at t₂ of F₂ =C₁ +2C₂ ;

Equation (17) is rearranged as follows:

    Tln R+TlnF.sub.i =t.sub.i +Tln C.sub.t                     (21)

    t.sub.i =T(1n R-1n C.sub.t)+Tln F.sub.i =a+b 1n F.sub.i    (22)

    t.sub.1 =a+b ln(C.sub.1 +C.sub.2)                          (23)

    t.sub.2 =a+b ln(C.sub.1 +2C.sub.2)                         (24)

    C.sub.1 +C.sub.2 =ln.sup.-1 (t.sub.1 /b-a/b)=K.sub.1       (25)

    C.sub.1 +2C.sub.2 =ln.sup.-1 (t.sub.2 /b-a/b)=K.sub.2      (26)

    C.sub.2 =K.sub.2 -K.sub.1                                  (27)

    C.sub.1 =K.sub.1 -C.sub.2 =K.sub.1 -(K.sub.2 -K.sub.1)=2K.sub.1 -K.sub.2(28)

and using system constants which are:

C_(t) =0.001 mole/liter

R=0.0816

Estimated from measurements

T=4.57 min.

R=ln⁻¹ (a/b+ln C_(t))=0.0945

Calculated from experimental data,

T=b=4.71 min.

The following example of data was obtained in Table I.

                                      TABLE I                                     __________________________________________________________________________                                 Calculated                                       100 C.sub.1                                                                       100 C.sub.2                                                                        -1n F.sub.1                                                                        -1n F.sub.2                                                                        t.sub.1                                                                            t.sub.2                                                                            100 C.sub.1                                                                        100 C.sub.2                                 __________________________________________________________________________    1.2 0.3962                                                                             4.1375                                                                             3.9158                                                                              1.875                                                                              3.063                                                                             1.124                                                                              0.453                                       1.2 0.7925                                                                             3.9158                                                                             3.5809                                                                              3.075                                                                              4.713                                                                             1.188                                                                              0.847                                       1.5 1.3019                                                                             3.5749                                                                             3.1933                                                                              4.730                                                                              6.470                                                                             1.598                                                                              1.295                                       2.6 0.3962                                                                             3.5078                                                                             3.3836                                                                              4.563                                                                              5.375                                                                             2.266                                                                              0.526                                       2.4 0.7925                                                                             3.4444                                                                             3.2226                                                                              5.117                                                                              6.217                                                                             2.314                                                                              0.827                                       2.1 1.9057                                                                             3.2175                                                                             2.8283                                                                              6.063                                                                              7.713                                                                             2.227                                                                              1.613                                       8.8 0.6038                                                                             2.3641                                                                             2.3018                                                                             10.016                                                                             10.392                                                                             8.157                                                                              0.740                                       8.7 0.8962                                                                             2.3438                                                                             2.2545                                                                             10.225                                                                             10.706                                                                             8.300                                                                              1.001                                       9.0 1.8019                                                                             2.2254                                                                             2.0712                                                                             10.983                                                                             11.683                                                                             9.175                                                                              1.753                                       3.6 4.3962                                                                             2.5262                                                                             2.0881                                                                              9.767                                                                             11.650                                                                             4.286                                                                              4.153                                       4.6 0.8019                                                                             2.9184                                                                             2.7800                                                                              7.750                                                                              8.467                                                                             4.592                                                                              0.905                                       4.4 2.0000                                                                             2.7489                                                                             2.4769                                                                              8.763                                                                             10.050                                                                             4.672                                                                              2.145                                       __________________________________________________________________________

Where concentration C_(i) is mole/liter and time t_(i) is minutes.

The linear relationship of this multiple endpoint system is graphicallydepicted in FIG. 3.

Statement of Intent

The inventor hereby states his intent to rely on the Doctrine ofEquivalents to determine and assess the fair scope of his invention asset out and defined in the following claims.

What is claimed is:
 1. A mixing cell comprising:(a) a body defining achamber having a means for introduction of solution to said chamber anda means for exciting of solution from said chamber where introduction ofsaid solution takes place in the chamber at a lower level than exit ofsaid solution; (b) a sensing means positioned to be in contact with saidsolution in said chamber; (c) a modified Spinfin™ type stirrerpositioned in said chamber, said stirrer modified by removal of top finsand addition of side slots.
 2. The mixing cell of claim 1 wherein saidchamber narrows near the solution exit region to facilitate the removalof bubbles.
 3. The mixing cell of claim 1 wherein said chamber has afixed volume.
 4. The mixing cell of claim 1 wherein said sensing meansis a potentiometric electrode.
 5. The mixing cell of claim 1 whereinsaid sensing means is an amperometric electrode.